*Please excuse my absolute ignorance, but I was under the impression that classical information channel was only required to transmit one of the entangled photons. If one of the entangled photons (or what ever it is that is entangled) was transported elsewhere (truck, fiber optics, what-not) the two entangled would still maintain the same state (spin etc) and information could then be transmitted faster than light by changing the state of one and reading the state of the other.*

Information cannot be transmitted faster than light as far as we know in standard physics today (barring extreme relativistic things like white or black holes and I doubt even those unless/until experiment verifies any claim that they can).

Quantum theory doesn't get around it. You cannot choose the direction to "collapse" or "change the state" of one of the two entangled spins, because the instant you measure it, it "collapses". You might now be able to predict the state of the other end of the channel, but the person there can't because he doesn't know what you measured, so if he measures up or down when he tries (again, supposed "collapsing the wavefunction") he won't know what you measured at your end or (since the two spins are no longer entangled as soon as a measurement is made at either end) what you do to it subsequently.

But the real problem (the "paradox" bit of EPR) is much worse than that. Suppose the two "entangled" electrons are separated by some distance D. Non-relativistic naive stupid quantum theory states that when one of the two electrons is measured, the wavefunction of the whole thing collapses. But suppose that D is nice and large -- in gedanken experiments we can make it a light year, why not? In the "rest frame of the Universe" (the frame in which the cosmic microwave background has on average no directional doppler shift) experimenters on *both* ends *simultaneously* perform a measurement of the spin state of the two electrons. This (simultaneity) is a perfectly valid concept in any *given* frame but is not a frame invariant concept. Neither is temporal ordering a universally valid concept. But given a simultaneous measurement of the two spins, which measurement causes the wavefunction to collapse and determines the global final state, given that the entropy of their measuring apparatus (which is responsible for the random phase shifts that supposedly break the entanglement, see Nakajima-Zwanzig equation and the Generalized Master Equation) is supposedly completely separable and independent?

By making D nice and large, we have a further problem. I said that the measurements were simultaneous in "the rest frame" (and even gave you a prescription for determining what frame I mean), but that means that if we boost that coordinate frame along one direction or the other, we can make *either measurement occur first!* That is, suppose the spins are in a singlet spin state so that if one is measured up (along some axis) the other must be measured down. Suppose that in frame A, spin 1 interacts with its local measuring apparatus *first* and is filtered into spin down. This interaction with its *local* entropy pool -- exchanging information with it via strictly retarded e.g. electromagnetic interactions -- supposedly "transluminally", that is to say *instantaneously in frame A* -- "causes" (whatever you want that word to mean) spin 2 in frame A to collapse into a non-entangled quantum state in which the probability of measuring its spin up in that frame some time later than the time of measurement in frame A is unity. In frame B, however, it is spin 2's measurement that is performed first, and as the electron interacts with *its* entropy pool you have a serious problem. If you follow *any* of the quantum approaches to measurement -- most of them random phase approximation or master equation projections that assume that the filter forces a final state on the basis of its local entropy and unknown/unspecified state -- it *cannot* independently conclude that the spin of this electron is down -- the measurement will definitely be up -- because in frame A the measurement of spin 1 has already happened. In no possible sense can the measurement of spin 2 in frame B in the up state "cause" spin 1 to be in a state that -- independent of the state of its measurement apparatus -- will definitely be measured as spin down. Otherwise you have (in frame A) to accept the truth of the statement that a *future* measurement of the state of spin 2 is what determines the outcome of the *present* measurement of the state of spin 1. Oooo, bad.

The problem, as you can see, is that relativity theory puts some very stringent limits on what we can possibly mean by the word "cause". They pretty much completely exclude any possible way that the statement "measuring spin 1 **causes** the 1-2 entangled wavefunction **to collapse**" can have frame-invariant meaning, and meaning that isn't inertial frame invariant in a relativistic universe isn't, that is, it is meaningless. We can only conclude that the correlated outcomes of the measurements was not determined by the *local* entropy state of the measurement apparatus *at the time of the measurements*.

Fortunately, we have one more tool to help us understand the outcome. Physics is symmetric in time. Indeed, our insistence on using retarded vs advanced or stationary (Dirac) Green's functions to describe causal interactions is entirely due to our psychological/perceptual experience of an *entropic* arrow of time, where entropy is strictly speaking the log of the missing/lost/neglected information in any *macroscopic* description of a *microscopically reversible* problem. That's the reason the Generalized Master Equation approach is so enormously informative. It starts with the *entire, microscopically reversible Universe*, which is *all* in a definite quantum entangled state with *nothing outside of it* to cause it to "collapse". In this "God's Eye" description, there is just a Universal wavefunction or density operator for a few gazillion particles with completely determined phases, evolving completely reversibly in time, with zero entropy. One then takes some subsystem -- say, an innocent pair of unsuspecting electrons -- and forms the e.g. 2x2 submatrix describing their mutually coupled state. Note well that *both spins are coupled to every other particle in the Universe at all times* -- this submatrix is "identified", not really created or derived, within the larger universal density matrix, and things like rows and columns can be permuted to (without loss of generality) bring it to the upper left hand corner where it becomes the "system". The submatrix for everything else (not including coupling to the spins) is similarly identified.

Nakajima-Zwanzig construction treats this second submatrix *statistically* because we *cannot know or measure the general state of the Universe* and have a hard enough time measuring/knowing the state of the 2x2 submatrix we've identified as an "entangled system". It projects the entirety of "everything else" into *diagonal probabilities* (by e.g. a random phase approximation, making the entropy of the rest of the Universe *classical* entropy) and then treats the interaction of these diagonal objects with the spins as being weak enough to be ignored, usually, except of course when it is not. It is not when e.g. the spins emit or absorb photons from the rest of the Universe (virtual or otherwise) while interacting with a measuring apparatus or the apparatus that prepared the spins. Because we cannot track the actual *fully* entangled phases of all the interactions in this enormous submatrix and with the submatrix and the system, the best we can manage is this semiclassical interaction that takes entropy from "the bath" (everything else) and bleeds it *statistically* into "the system".

In this picture (which should again be geometrically relativistic) there was never any question as to the outcome of the "measurement" of the entangled spin state by the remotely separated apparati, and furthermore, while the NZ equation is not reversible, we can fully appreciate the fact that if we time reverse the actual density matrix it approximates, the two electrons will leap out of the measuring apparatus, propagate backwards in time, and form the original supposedly quantum entangled state because *it never left it* -- it was/is/will be entangled with every particle that makes up the measuring apparatus that would eventually "collapse" its wavefunction over the entire span of time.

Note that in this description there is no such thing as wavefunction collapse, not really. That whole idea is neither microreversible nor frame invariant. It describes the *classical* process of measurement of a quantum object, where the measuring apparatus is not treated either relativistically correctly or as a fully coupled quantum system in in a *collectively* definite state in its own right. It isn't surprising that it leads to paradoxes and hence silly statements that don't really describe what is going on.

This is a more detailed discussion of the very apropos comment above that similarly resolves Schrodinger's Cat -- the cat cannot be in a quantum superposition of alive and dead because every particle in the cat and the quantum decaying nucleus that triggers the infernal device is *never* isolated from *every other particle in the Universe*. The cat gives off thermal radiation as it is alive that exchanges information and entropy with the walls of the death chamber, which interact thermally with the outside. The *instant* the cat dies, there is a retarded propagation of the altered trajectories of all of its particles communicated to the outside Universe of coupled particles, which were in turn communicating/interacting with all of the particles that make up "the cat" and with the nucleus itself and with the detector and with the poisoning device both before, during, and after all changes. the changes never occur in the "isolation" we approximate and imagine to simplify the problem.

Hope this helps.

rgb